$\begin{array}{l}
\left(\begin{array}{llll}
1 & 3 & 8 & 5 \\
5 & 4 & 6 & 2 \\
6 & 7 & 1 & 8 \\
2 & 9 & 3 & 7
\end{array}\right) \\
a _{34}=
\end{array}$
Answer (1)
Identify the 3rd row and 4th column of the matrix.
Locate the element at the intersection of the 3rd row and 4th column.
The element a 34 is 8.
Therefore, the answer is 8 .
Explanation
Understanding the Problem We are given a 4x4 matrix and asked to find the element a 34 , which represents the element in the 3rd row and 4th column of the matrix.
Identifying the Row and Column The given matrix is: ( 1 3 8 5 5 4 6 2 6 7 1 8 2 9 3 7 ) To find the element a 34 , we need to identify the 3rd row and the 4th column.
Locating the Element The 3rd row of the matrix is: 6 7 1 8 The 4th column of the matrix is: 5 2 8 7
Determining the Value The element that is in both the 3rd row and the 4th column is 8. Therefore, a 34 = 8 .
Examples
Matrices are used in various fields such as computer graphics, physics, and engineering. For example, in computer graphics, matrices are used to represent transformations of objects in 3D space, such as rotations, scaling, and translations. Understanding how to identify elements within a matrix is crucial for performing these transformations correctly. In physics, matrices are used to describe systems of linear equations, which can be used to model a wide range of physical phenomena.
